Topological lattice defects violate a crystalline symmetry locally while the rest of the lattice remains locally indistinguishable from a defect-free lattice.
They can be constructed by cutting and gluing symmetry-related sections of the lattice by means of a Volterra process [1]}, [2]}, [3]}, [4]}.
Topological lattice defects are characterized by their holonomy, which is defined as the action on a local coordinate system transported around the defect.
Common examples are dislocations and disclinations.
The latter violate rotation symmetry locally and carry a rotation holonomy.
The association to a holonomy is the property that distinguishes topological lattice defects from other lattice defects.
For example, atomic defects such as vacancies, substitutions, or atoms at interstitial positions are not associated to a holonomy, and therefore are not considered topological.
For grain boundaries separating regions of different lattice orientations, it has been suggested that they can be described as arrays of dislocations [5]}, [6]}, [7]} or disclinations [8]}, [9]}, [10]}, [11]}, [12]}, [13]}.
